Co-Optimization of Design and Fabrication Plans for Carpentry: Supplemental Material

TL;DR

This paper introduces a novel bi-level optimization approach for jointly designing and fabricating carpentry objects, leveraging e-graphs and a feedback-guided search to efficiently explore complex design spaces.

Contribution

It adapts program synthesis techniques to optimize both design and fabrication plans simultaneously, addressing intractability with a new BOP e-graph representation and ICEE search strategy.

Findings

Efficient joint optimization of design and fabrication plans demonstrated.

BOP e-graphs reduce redundant computations across design variants.

ICEE search effectively manages e-graph size and guides optimization.

Abstract

Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design, instead considering families of design variations, sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts(BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manage-able and direct the search toward promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.